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August 17, 2010

Doing the “Math” – Part 2

Nick Diaz

Many of us in Frederick County have had our fill of the failures of TERC Investigations and other such “constructivist” programs that de-emphasize the teaching of traditional algorithms. I finished my last article by asking the following question:


“Is switching back to traditional math curriculum the simple answer?”


Traditional math has its own baggage. The derogatory term “drill and kill” came about, at least in part, because of unending dittos full of math problems divorced from any meaning. Interminable drills in multiplication and other operations may serve to help children memorize math facts, but they can also serve to deaden any interest in pursuing the field further.


While a certain amount of memorization is inevitable, is there no better way to present a given lesson? What about students who are not strong in memorization skills, or who struggle with traditional computational methods? Constructivist math has attempted to answer this problem, but traditional methods offer little guidance.


Traditional programs have a strict focus on accuracy and efficiency – certainly two critical matters when it comes to math. The computational methods stressed in traditional programs are taught because they have been found to be the quickest and most efficient means of getting the correct answer.


Imagine a carpenter laying out stair stringers, or a shopper figuring the cost per pound of a product, or a manufacturing clerk taking a quick inventory. Time and accuracy are at a premium to these people, and constructivist methods are of little use. To suggest, for example, that adults in real life circumstances would draw a grid, giving each box a diagonal, and then slog through the “lattice” method of multiplication instead of using the traditional pencil-and-paper method, (or simply grabbing a calculator), is pure folly. The boss is waiting, time is money, and there are bigger fish to fry.


Yet, traditional math curriculum is also legitimately criticized for avoiding the questions of developmental ability, of individual differences among students, and, ultimately, of sheer boredom. In traditional programs, one size fits all, even when it doesn’t. In traditional programs, memorization and mind-numbing repetition are the minimum height for the mathematical carnival ride, even when a given student may be too short.


Instead of connecting mathematics with real life and offering meaningful reasons for students to do computations, traditional programs often fall back on the unspoken expression “because you have to, that’s why.” It should also be noted that the other areas of curriculum which once helped students understand the value of math skills, such as industrial arts, home economics, and physical education, are cut back or missing from modern schools. Learning math just for the sake of math will only appeal to a small fraction of the student population.


What is our answer, then? If constructivist math programs have laudable goals of reaching out to each student, of providing differentiation and of offering a deeper view of math, it is in the execution where the programs have failed. By ignoring real world circumstances and developmental growth over grade levels, constructivist math programs can bog down students in pointless techniques and processes and stifle chances for later success in math. Many parents may find their children going ever sideways, and never forward.


Constructivist math programs may look good on the drawing board, but they can be slippery where the rubber meets the road. Traditional programs don’t fare much better. By focusing on memorization rather than meaning, and by failing to provide the means for differentiation between students, traditional programs offer achievement for those interested in numbers for the sake of numbers, but defeat for many other students.


Teachers in the classroom have offered the closest thing to an answer, and this fact also explains why some communities become bitterly opposed to constructivist programs and other communities tolerate the programs. In many districts, teachers simply do not follow the Everyday Math and similar programs as closely as the designers would have preferred. These teachers mix in traditional methods. They leave out or minimize troublesome features. They take it upon themselves to differentiate in their classroom while making certain all the children meet a minimum standard for real world performance.


In short, they do their own thing. Oh, my goodness – whoever heard of such a thing! Such behavior can sometimes drive administrators up a wall, and it often gets the teachers, those who pride in thinking for themselves, in trouble with principals and supervisors. On the other hand, teachers are and should be the buffer between children and stupidity. This mix between traditional and constructivist ideas and methods might be the compromise and the solution.


Except for a couple of problems:


First, in some states and some districts formal or standardized tests used to gauge mathematical achievement necessitate a thorough understanding of constructivist methods for a child to score well. The New York State Regents exam is one example. Children may score well on the tests, but they fail when it comes to real world computation or higher order math classes in later grades. Students win and lose at the same time.


Second, school administrators make the somewhat valid point that 50 teachers doing their own thing means one thousand students with differing standards of mathematical knowledge and achievement. The teachers are making the best of a bad situation, but leadership must eventually unite such efforts.


In the end, there must be unification of the constructivist goals of deeper understanding and meaningful connections and the traditionalist goals of accuracy and efficiency. Frankly, neither side has distinguished itself in nationally used programs, but somewhere there must be someone who can solve this equation.


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